In this paper,we study the category of corepresentations of a monoidal comonad.We show that it is a semisimple category if and only if the monoidal comonad is a cosemisipmle(coseparable)comonad,and it is a braided cat...In this paper,we study the category of corepresentations of a monoidal comonad.We show that it is a semisimple category if and only if the monoidal comonad is a cosemisipmle(coseparable)comonad,and it is a braided category if and only if the monoidal comonad admit a cobraided structure.At last,as an application,the braided structure and the semisimplicity of the Hom-comodule category of a monoidal Hom-bialgebra are discussed.展开更多
We investigate how the category of comodules of bimonads can be made into a monoidal category.It suffices that the monad and comonad in question are bimonads,with some extra compatibility relation.On a monoidal catego...We investigate how the category of comodules of bimonads can be made into a monoidal category.It suffices that the monad and comonad in question are bimonads,with some extra compatibility relation.On a monoidal category of comodules of bimonads,we cons true t a braiding and get the necessary and sufficien t conditions making it a braided monoidal category.As an application,we consider the category of comodules of corings and the category of entwined modules.展开更多
基金the National Natural Science Foundation of China(Nos.11626138,11626139)the Natural Science Foundation of Shandong Province(No.ZR2016AQ03).
文摘In this paper,we study the category of corepresentations of a monoidal comonad.We show that it is a semisimple category if and only if the monoidal comonad is a cosemisipmle(coseparable)comonad,and it is a braided category if and only if the monoidal comonad admit a cobraided structure.At last,as an application,the braided structure and the semisimplicity of the Hom-comodule category of a monoidal Hom-bialgebra are discussed.
基金Supported by the National Natural Science Foundation of China(No.11601486)Foundation of Zhejiang Educational Commitee(No.Y201738645)Project of Zhejiang College,Shanghai University of Finance and Economics(No.2018YJYB01).
文摘We investigate how the category of comodules of bimonads can be made into a monoidal category.It suffices that the monad and comonad in question are bimonads,with some extra compatibility relation.On a monoidal category of comodules of bimonads,we cons true t a braiding and get the necessary and sufficien t conditions making it a braided monoidal category.As an application,we consider the category of comodules of corings and the category of entwined modules.
